10 citations · 17 across the 10 of their papers we have counts for
13 papers
Mixing of the BCZ Map
Albert Artiles, Andrew Best, Matteo Bordignon
We prove that the Boca--Cobeli--Zaharescu (BCZ) map is strongly mixing with respect to normalized Lebesgue measure on the BCZ triangle.
On the Polynomial Szemerédi Theorem in Finite Commutative Rings
Vitaly Bergelson, Andrew Best
The polynomial Szemerédi theorem implies that, for any , any family of nonconstant polynomials with constant term zero, and…
Polynomial ergodic averages for certain countable ring actions
Andrew Best, Andreu Ferré Moragues
A recent result of Frantzikinakis establishes sufficient conditions for joint ergodicity in the setting of -actions. We generalize this result for actions of second-cou…
Multiple recurrence and large intersections for abelian group actions
Ethan Ackelsberg, Vitaly Bergelson, Andrew Best
The purpose of this paper is to study the phenomenon of large intersections in the framework of multiple recurrence for measure-preserving actions of countable abelian groups. Amon…
The Furstenberg-Sárközy Theorem and Asymptotic Total Ergodicity Phenomena in Modular Rings
Vitaly Bergelson, Andrew Best
The Furstenberg-Sárközy theorem asserts that the difference set of a subset with positive upper density intersects the image set of any polynomial $P \…
Sums of Powers in Large Finite Fields: A Mix of Methods
Vitaly Bergelson, Andrew Best, Alex Iosevich
Can any element in a sufficiently large finite field be represented as a sum of two th powers in the field? In this article, we recount some of the history of this problem, touc…
Ramsey Theory Problems over the Integers: Avoiding Generalized Progressions
Andrew Best, Karen Huan, Nathan McNew +4
Two well studied Ramsey-theoretic problems consider subsets of the natural numbers which either contain no three elements in arithmetic progression, or in geometric progression. We…
The emergence of 4-cycles in polynomial maps over the extended integers
Andrew Best, Patrick Dynes, Steven J. Miller +2
Let ; for each integer it is interesting to consider the number of iterates , if possible, needed to satisfy . The sets $\{α, f(α),…
Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers , with initial terms . Previo…
Benford Behavior of Generalized Zeckendorf Decompositions
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
We prove connections between Zeckendorf decompositions and Benford's law. Recall that if we define the Fibonacci numbers by and , every…
Geometric-progression-free sets over quadratic number fields
Andrew Best, Karen Huan, Nathan McNew +4
A problem of recent interest has been to study how large subsets of the natural numbers can be while avoiding 3-term geometric progressions. Building on recent progress on this pro…
Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers , with initial terms . We con…
Benford Behavior of Zeckendorf Decompositions
Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5
A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers . A set $S \subset \…